Jeremy likes to paint. He estimates the number of paintings he completes using the function, P(w) = 1/3w + 4, where w is the number of weeks he spends painting. The function J(y) represents how many weeks per year he spends painting. Which composite function would represent how many paintings Jeremy completes in a year?

a.) P[J(y)] = J(1/3w + 4)
b.) J[P(w)] = 1/3 ⋅ J + 4
c.) P[J(y)] = 1/3 ⋅ J(y) + 4
d.) J[P(w)] = J(1/3w + 4)

9514 1404 393

  c.)  P[J(y)] = 1/3 ⋅ J(y) + 4

Step-by-step explanation:

The function P takes a number of weeks as an argument and returns the number of paintings.

The function J takes some argument (unspecified) and returns a number of weeks per year.

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The composite function that will give the number of paintings per year will be P(weeks per year) = P(J(y)).

  P(J(y)) = 1/3·J(y) +4 . . . . . matches choice C

Additional comment

Looking at the units of the input and output of each of the functions is called "units analysis." It is a good way to solve many problems.

spinning a 1, 2, or 3. option d.

step-by-step explanation: when spinning a number graph up to 4, and aiming for any number less than 3, that automatically eliminates the number 4. now you have two numbers to spin on that are less than 3, but the number 3 is included in this question because it's no greater of an number than itself. i hope this you : )